return { 
3,
12,
21,
111,
111111,
11112,
11121,
11211,
12111,
21111,
1122,
1212,
1221,
2112,
2121,
2211,
222,
1113,
1131,
1311,
3111,
123,
132,
213,
231,
312,
321,
33,
114,
141,
411,
24,
42,
111111111,
11111112,
11111121,
11111211,
11112111,
11121111,
11211111,
12111111,
21111111,
1111122,
1111212,
1111221,
1112112,
1112121,
1112211,
1121112,
1121121,
1121211,
1122111,
1211112,
1211121,
1211211,
1212111,
1221111,
2111112,
2111121,
2111211,
2112111,
2121111,
2211111,
111222,
112122,
112212,
112221,
121122,
121212,
121221,
122112,
122121,
122211,
211122,
211212,
211221,
212112,
212121,
212211,
221112,
221121,
221211,
222111,
12222,
21222,
22122,
22212,
22221,
1111113,
1111131,
1111311,
1113111,
1131111,
1311111,
3111111,
111123,
111132,
111213,
111231,
111312,
111321,
112113,
112131,
112311,
113112,
113121,
113211,
121113,
121131,
121311,
123111,
131112,
131121,
131211,
132111,
211113,
211131,
211311,
213111,
231111,
311112,
311121,
311211,
312111,
321111,
11223,
11232,
11322,
12123,
12132,
12213,
12231,
12312,
12321,
13122,
13212,
13221,
21123,
21132,
21213,
21231,
21312,
21321,
22113,
22131,
22311,
23112,
23121,
23211,
31122,
31212,
31221,
32112,
32121,
32211,
2223,
2232,
2322,
3222,
11133,
11313,
11331,
13113,
13131,
13311,
31113,
31131,
31311,
33111,
1233,
1323,
1332,
2133,
2313,
2331,
3123,
3132,
3213,
3231,
3312,
3321,
333,
111114,
111141,
111411,
114111,
141111,
411111,
11124,
11142,
11214,
11241,
11412,
11421,
12114,
12141,
12411,
14112,
14121,
14211,
21114,
21141,
21411,
24111,
41112,
41121,
41211,
42111,
1224,
1242,
1422,
2124,
2142,
2214,
2241,
2412,
2421,
4122,
4212,
4221,
1134,
1143,
1314,
1341,
1413,
1431,
3114,
3141,
3411,
4113,
4131,
4311,
234,
243,
324,
342,
423,
432,
144,
414,
441,
111111222,
111112122,
111112212,
111112221,
111121122,
111121212,
111121221,
111122112,
111122121,
111122211,
111211122,
111211212,
111211221,
111212112,
111212121,
111212211,
111221112,
111221121,
111221211,
111222111,
112111122,
112111212,
112111221,
112112112,
112112121,
112112211,
112121112,
112121121,
112121211,
112122111,
112211112,
112211121,
112211211,
112212111,
112221111,
121111122,
121111212,
121111221,
121112112,
121112121,
121112211,
121121112,
121121121,
121121211,
121122111,
121211112,
121211121,
121211211,
121212111,
121221111,
122111112,
122111121,
122111211,
122112111,
122121111,
122211111,
211111122,
211111212,
211111221,
211112112,
211112121,
211112211,
211121112,
211121121,
211121211,
211122111,
211211112,
211211121,
211211211,
211212111,
211221111,
212111112,
212111121,
212111211,
212112111,
212121111,
212211111,
221111112,
221111121,
221111211,
221112111,
221121111,
221211111,
222111111,
11112222,
11121222,
11122122,
11122212,
11122221,
11211222,
11212122,
11212212,
11212221,
11221122,
11221212,
11221221,
11222112,
11222121,
11222211,
12111222,
12112122,
12112212,
12112221,
12121122,
12121212,
12121221,
12122112,
12122121,
12122211,
12211122,
12211212,
12211221,
12212112,
12212121,
12212211,
12221112,
12221121,
12221211,
12222111,
21111222,
21112122,
21112212,
21112221,
21121122,
21121212,
21121221,
21122112,
21122121,
21122211,
21211122,
21211212,
21211221,
21212112,
21212121,
21212211,
21221112,
21221121,
21221211,
21222111,
22111122,
22111212,
22111221,
22112112,
22112121,
22112211,
22121112,
22121121,
22121211,
22122111,
22211112,
22211121,
22211211,
22212111,
22221111,
1122222,
1212222,
1221222,
1222122,
1222212,
1222221,
2112222,
2121222,
2122122,
2122212,
2122221,
2211222,
2212122,
2212212,
2212221,
2221122,
2221212,
2221221,
2222112,
2222121,
2222211,
222222,
111111123,
111111132,
111111213,
111111231,
111111312,
111111321,
111112113,
111112131,
111112311,
111113112,
111113121,
111113211,
111121113,
111121131,
111121311,
111123111,
111131112,
111131121,
111131211,
111132111,
111211113,
111211131,
111211311,
111213111,
111231111,
111311112,
111311121,
111311211,
111312111,
111321111,
112111113,
112111131,
112111311,
112113111,
112131111,
112311111,
113111112,
113111121,
113111211,
113112111,
113121111,
113211111,
121111113,
121111131,
121111311,
121113111,
121131111,
121311111,
123111111,
131111112,
131111121,
131111211,
131112111,
131121111,
131211111,
132111111,
211111113,
211111131,
211111311,
211113111,
211131111,
211311111,
213111111,
231111111,
311111112,
311111121,
311111211,
311112111,
311121111,
311211111,
312111111,
321111111,
11111223,
11111232,
11111322,
11112123,
11112132,
11112213,
11112231,
11112312,
11112321,
11113122,
11113212,
11113221,
11121123,
11121132,
11121213,
11121231,
11121312,
11121321,
11122113,
11122131,
11122311,
11123112,
11123121,
11123211,
11131122,
11131212,
11131221,
11132112,
11132121,
11132211,
11211123,
11211132,
11211213,
11211231,
11211312,
11211321,
11212113,
11212131,
11212311,
11213112,
11213121,
11213211,
11221113,
11221131,
11221311,
11223111,
11231112,
11231121,
11231211,
11232111,
11311122,
11311212,
11311221,
11312112,
11312121,
11312211,
11321112,
11321121,
11321211,
11322111,
12111123,
12111132,
12111213,
12111231,
12111312,
12111321,
12112113,
12112131,
12112311,
12113112,
12113121,
12113211,
12121113,
12121131,
12121311,
12123111,
12131112,
12131121,
12131211,
12132111,
12211113,
12211131,
12211311,
12213111,
12231111,
12311112,
12311121,
12311211,
12312111,
12321111,
13111122,
13111212,
13111221,
13112112,
13112121,
13112211,
13121112,
13121121,
13121211,
13122111,
13211112,
13211121,
13211211,
13212111,
13221111,
21111123,
21111132,
21111213,
21111231,
21111312,
21111321,
21112113,
21112131,
21112311,
21113112,
21113121,
21113211,
21121113,
21121131,
21121311,
21123111,
21131112,
21131121,
21131211,
21132111,
21211113,
21211131,
21211311,
21213111,
21231111,
21311112,
21311121,
21311211,
21312111,
21321111,
22111113,
22111131,
22111311,
22113111,
22131111,
22311111,
23111112,
23111121,
23111211,
23112111,
23121111,
23211111,
31111122,
31111212,
31111221,
31112112,
31112121,
31112211,
31121112,
31121121,
31121211,
31122111,
31211112,
31211121,
31211211,
31212111,
31221111,
32111112,
32111121,
32111211,
32112111,
32121111,
32211111,
1112223,
1112232,
1112322,
1113222,
1121223,
1121232,
1121322,
1122123,
1122132,
1122213,
1122231,
1122312,
1122321,
1123122,
1123212,
1123221,
1131222,
1132122,
1132212,
1132221,
1211223,
1211232,
1211322,
1212123,
1212132,
1212213,
1212231,
1212312,
1212321,
1213122,
1213212,
1213221,
1221123,
1221132,
1221213,
1221231,
1221312,
1221321,
1222113,
1222131,
1222311,
1223112,
1223121,
1223211,
1231122,
1231212,
1231221,
1232112,
1232121,
1232211,
1311222,
1312122,
1312212,
1312221,
1321122,
1321212,
1321221,
1322112,
1322121,
1322211,
2111223,
2111232,
2111322,
2112123,
2112132,
2112213,
2112231,
2112312,
2112321,
2113122,
2113212,
2113221,
2121123,
2121132,
2121213,
2121231,
2121312,
2121321,
2122113,
2122131,
2122311,
2123112,
2123121,
2123211,
2131122,
2131212,
2131221,
2132112,
2132121,
2132211,
2211123,
2211132,
2211213,
2211231,
2211312,
2211321,
2212113,
2212131,
2212311,
2213112,
2213121,
2213211,
2221113,
2221131,
2221311,
2223111,
2231112,
2231121,
2231211,
2232111,
2311122,
2311212,
2311221,
2312112,
2312121,
2312211,
2321112,
2321121,
2321211,
2322111,
3111222,
3112122,
3112212,
3112221,
3121122,
3121212,
3121221,
3122112,
3122121,
3122211,
3211122,
3211212,
3211221,
3212112,
3212121,
3212211,
3221112,
3221121,
3221211,
3222111,
122223,
122232,
122322,
123222,
132222,
212223,
212232,
212322,
213222,
221223,
221232,
221322,
222123,
222132,
222213,
222231,
222312,
222321,
223122,
223212,
223221,
231222,
232122,
232212,
232221,
312222,
321222,
322122,
322212,
322221,
11111133,
11111313,
11111331,
11113113,
11113131,
11113311,
11131113,
11131131,
11131311,
11133111,
11311113,
11311131,
11311311,
11313111,
11331111,
13111113,
13111131,
13111311,
13113111,
13131111,
13311111,
31111113,
31111131,
31111311,
31113111,
31131111,
31311111,
33111111,
3321111,
112233,
112323,
112332,
113223,
113232,
113322,
121233,
121323,
121332,
122133,
122313,
122331,
123123,
123132,
123213,
123231,
123312,
123321,
131223,
131232,
131322,
132123,
132132,
132213,
132231,
132312,
132321,
133122,
133212,
133221,
211233,
211323,
211332,
212133,
212313,
212331,
213123,
213132,
213213,
213231,
213312,
213321,
221133,
221313,
221331,
223113,
223131,
223311,
231123,
231132,
231213,
231231,
231312,
231321,
232113,
232131,
232311,
233112,
233121,
233211,
311223,
311232,
311322,
312123,
312132,
312213,
312231,
312312,
312321,
313122,
313212,
313221,
321123,
321132,
321213,
321231,
321312,
321321,
322113,
322131,
322311,
323112,
323121,
323211,
331122,
331212,
331221,
332112,
332121,
332211,
22233,
22323,
22332,
23223,
23232,
23322,
32223,
32232,
32322,
33222,
111333,
113133,
113313,
113331,
131133,
131313,
131331,
133113,
133131,
133311,
311133,
311313,
311331,
313113,
313131,
313311,
331113,
331131,
331311,
333111,
12333,
13233,
13323,
13332,
21333,
23133,
23313,
23331,
31233,
31323,
31332,
32133,
32313,
32331,
33123,
33132,
33213,
33231,
33312,
33321,
3333,
111111114,
111111141,
111111411,
111114111,
111141111,
111411111,
114111111,
141111111,
411111111,
11111124,
11111142,
11111214,
11111241,
11111412,
11111421,
11112114,
11112141,
11112411,
11114112,
11114121,
11114211,
11121114,
11121141,
11121411,
11124111,
11141112,
11141121,
11141211,
11142111,
11211114,
11211141,
11211411,
11214111,
11241111,
11411112,
11411121,
11411211,
11412111,
11421111,
12111114,
12111141,
12111411,
12114111,
12141111,
12411111,
14111112,
14111121,
14111211,
14112111,
14121111,
14211111,
21111114,
21111141,
21111411,
21114111,
21141111,
21411111,
24111111,
41111112,
41111121,
41111211,
41112111,
41121111,
41211111,
42111111,
1111224,
1111242,
1111422,
1112124,
1112142,
1112214,
1112241,
1112412,
1112421,
1114122,
1114212,
1114221,
1121124,
1121142,
1121214,
1121241,
1121412,
1121421,
1122114,
1122141,
1122411,
1124112,
1124121,
1124211,
1141122,
1141212,
1141221,
1142112,
1142121,
1142211,
1211124,
1211142,
1211214,
1211241,
1211412,
1211421,
1212114,
1212141,
1212411,
1214112,
1214121,
1214211,
1221114,
1221141,
1221411,
1224111,
1241112,
1241121,
1241211,
1242111,
1411122,
1411212,
1411221,
1412112,
1412121,
1412211,
1421112,
1421121,
1421211,
1422111,
2111124,
2111142,
2111214,
2111241,
2111412,
2111421,
2112114,
2112141,
2112411,
2114112,
2114121,
2114211,
2121114,
2121141,
2121411,
2124111,
2141112,
2141121,
2141211,
2142111,
2211114,
2211141,
2211411,
2214111,
2241111,
2411112,
2411121,
2411211,
2412111,
2421111,
4111122,
4111212,
4111221,
4112112,
4112121,
4112211,
4121112,
4121121,
4121211,
4122111,
4211112,
4211121,
4211211,
4212111,
4221111,
112224,
112242,
112422,
114222,
121224,
121242,
121422,
122124,
122142,
122214,
122241,
122412,
122421,
124122,
124212,
124221,
141222,
142122,
142212,
142221,
211224,
211242,
211422,
212124,
212142,
212214,
212241,
212412,
212421,
214122,
214212,
214221,
221124,
221142,
221214,
221241,
221412,
221421,
222114,
222141,
222411,
224112,
224121,
224211,
241122,
241212,
241221,
242112,
242121,
242211,
411222,
412122,
412212,
412221,
421122,
421212,
421221,
422112,
422121,
422211,
22224,
22242,
22422,
24222,
42222,
1111134,
1111143,
1111314,
1111341,
1111413,
1111431,
1113114,
1113141,
1113411,
1114113,
1114131,
1114311,
1131114,
1131141,
1131411,
1134111,
1141113,
1141131,
1141311,
1143111,
1311114,
1311141,
1311411,
1314111,
1341111,
1411113,
1411131,
1411311,
1413111,
1431111,
3111114,
3111141,
3111411,
3114111,
3141111,
3411111,
4111113,
4111131,
4111311,
4113111,
4131111,
4311111,
111234,
111243,
111324,
111342,
111423,
111432,
112134,
112143,
112314,
112341,
112413,
112431,
113124,
113142,
113214,
113241,
113412,
113421,
114123,
114132,
114213,
114231,
114312,
114321,
121134,
121143,
121314,
121341,
121413,
121431,
123114,
123141,
123411,
124113,
124131,
124311,
131124,
131142,
131214,
131241,
131412,
131421,
132114,
132141,
132411,
134112,
134121,
134211,
141123,
141132,
141213,
141231,
141312,
141321,
142113,
142131,
142311,
143112,
143121,
143211,
211134,
211143,
211314,
211341,
211413,
211431,
213114,
213141,
213411,
214113,
214131,
214311,
231114,
231141,
231411,
234111,
241113,
241131,
241311,
243111,
311124,
311142,
311214,
311241,
311412,
311421,
312114,
312141,
312411,
314112,
314121,
314211,
321114,
321141,
321411,
324111,
341112,
341121,
341211,
342111,
411123,
411132,
411213,
411231,
411312,
411321,
412113,
412131,
412311,
413112,
413121,
413211,
421113,
421131,
421311,
423111,
431112,
431121,
431211,
432111,
12234,
12243,
12324,
12342,
12423,
12432,
13224,
13242,
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